A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

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(3) 14 m/s and 15 m/s. Given: radius of curvature R=20 m at the top of the hill. Idea: "weightlessness" means the seat pushes with no force at all, so gravity alone must supply the whole centripetal force. At that point N=0, so mg=(mv²)/R. The mass cancels: v²=gR. With g=10 m s⁻²: v²=200, so v=14.1 m/s. With g=9.8 m s⁻²: v=√196=14.0 m/s. Either way the speed lies between 14 and 15 m/s.

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

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